1. Plant size

Plant’s current size () — the larger the plant is, the more it adds every day.

Growth rate () — a general concept, which will be discussed in more detail below.

Cell size () — i.e. there is an upper limit for growth.

Thus, . When the plant is small, the upper limit is not important and the limiting factor is current size, so initially the plant grows [almost] exponentially. When the plant grows large, the upper limit becomes more binding and growth decelerates again. Let me solve this equation for .

Solving the left side integral:
So
Solving the right side integral:
Now putting it all together:
Simplify and redefine the constant:
Finally, making it discrete:

2. Growth rate

Time to discuss . The growth rate depends on:

(mis)match between the “climate requirements” of a particular species and “climate” or “resource endowment” of a particular cell

capacity to acquire resources — roots and leaves

For example, insufficient sunlight can be partly compensated by large leaves and insufficient minerals/water — by longer roots. Excessive resources will represent a small saving in roots/leaves, but will still be limiting the growth rate. As a possible way to make the impact of deficit and excess of resources to be symmetric, developing roots and leaves can cost no resources, just a mouse click and some waiting time. Have to think a bit on this.

Well, I tried writing up some code for it, but never went beyond designing a simple SQL database and a simple hex grid in PHP/HTML. What you see is all I have, no more than an idea. Anyway, I’m afraid the era of browser games is over, and a new game is probably not even worth thinking about.